WBJEE · Maths · Matrices
If \(A\) is a square matrix then,
- A \(\mathrm{A}+\mathrm{A}^{\mathrm{T}}\) is symmetric
- B \(\mathrm{AA}^{\mathrm{T}}\) is skew - symmetric
- C \(\mathrm{A}^{\mathrm{T}}+\mathrm{A}\) is skew-symmetric
- D \(\quad \mathrm{A}^{\mathrm{T}} \mathrm{A}\) is skew symmetric
Answer & Solution
Correct Answer
(A) \(\mathrm{A}+\mathrm{A}^{\mathrm{T}}\) is symmetric
Step-by-step Solution
Detailed explanation
Hints: \(\left(\mathrm{A}+\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\left(\mathrm{A}^{\mathrm{T}}\right)^{\mathrm{T}}=\mathrm{A}^{\mathrm{T}}+\mathrm{A}=\mathrm{A}+\mathrm{A}^{\mathrm{T}}\)
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